Off-Diagonal Two Weight Bumps for Fractional Sparse Operators

Abstract

In this paper, we continue some recent work on two weight boundedness of sparse operators to the "off-diagonal" setting. We use the new "entropy bumps" introduced in by Treil-Volberg ([21]) and improved by Lacey-Spencer ([9]) and the "direct comparison bumps" introduced by Rahm-Spencer ([19]) and improved by Lerner ([10]). Our results are "sharp" in the sense that they are sharp in various particular cases. A feature is that given the current machinery, the proofs are almost trivial.